01234_01243_01342_02134_02143_03124_12034_12043_13024_23014
Counting sequence:
1, 1, 2, 6, 24, 110, 533, 2663, 13637, 71380, 380737, 2062994, 11324291, 62839363, 351920038, 1986504140, 11290725857, 64561932719, 371151441260, 2143840393494, 12436159073588, 72418585847011, 423181708726311, 2480738741260187, 14584587597944232, 85973092849683393, 508036372248464431, 3008915095983671262, 17858124512097505501, 106195987091591678465, 632657807848004408539, 3775426640874015479147, 22565891018983797282335, 135078270339831650673949, 809703786110036867539209, 4860031089796560358484545, 29207317024182135339700509, 175733374156986986037555117, 1058520857362333279214372955, 6382663527306390250439244114, 38524635359130814620983698320, 232748886670716640748725774481, 1407437695475610801138127821496, 8518137711513713483420913024348, 51596085899404943614417343819066, 312773075609749864903604878628518, 1897437230635531435634441698460221, 11519055076043037364195811034060403, 69978477771102535989803725213767136, 425400470569569555514826594721567831, 2587650816653619366952354137037600742, 15749859792204219613489266632025545965, 95918140735782149739626562940915869879, 584477994564370966714838588788401191509, 3563442784656874175707588152428583239977, 21736869237205559406286745168226835359296, 132660492928875650254591921805052934821825, 810020296530672107596256643545942050168527, 4948260447847365051915371407097272109457983, 30241588954801282284534863167034444737059921, 184903644823051200046093563429832130692196562, 1131016341864553990321420334449317829331303080, 6921000314709591904543135018270774051717992954, 42368175777125682600971157104378278345572338535, 259463435452077577105941815656915832276360276832, 1589545315030137374744641862548118386118110857695, 9741483463467269722748866762548438379368768902615, 59721131042704733306904906901533524326174268965902, 366249642462941760671713188212946976562730808729241, 2246820445143170948713453278746084900147657142925838, 13787876878641753796287493580508938302291991498716064, 84637021679756914348437545314068595066525876176149417, 519700978175628228641400650437239064469223607779674906, 3192076405077313101184927424533739925735156528237656107, 19611740913728526780518689145889137431756878279086686580, 120525467614968432600464649613419729285164174967520282029, 740897496170523519072882222824805731674745716407224422322, 4555656745296956223867778858064507043847138505017274103111, 28019119599967161506509343496031071270541169738266487089946, 172371623776510798818245785329308339778524954320224173399316, 1060674520887003199866017435832136624305686883151433938754573, 6528312831169129031161908901473629188854017169196633369464960, 40190157928184640253927511014147980796154551984787487681608340, 247477643953297926632429554041486638395513607048717838781482780, 1524219083046055767411532978747284067088203525105991599605479521, 9389700049465007369733562065339382319071436231088398522378889189, 57855781787772010481799010023591613883059014662709080087897859841, 356558203373574778105595032992842649900614306816669434254843104194, 2197863346831515417360148623354343184450503747173948185741918257854, 13550507629778883900130790973781728361674871206843164464776547135634, 83558988105676481624351134591473466586112605430908093268286921625136, 515361146863207535843490016295683000582437682248600006523282978810198, 3179137394874061874283542924647644935139405469478438302239574596618504, 19614820007808072188141299890220703214179186227189680159353832652669636, 121041724585300533284991341722100206672536734109896506387433228113100397, 747067797990450251752739118411018707079987638142312190797140600536729060, 4611662455518071245842359433863619095691419257771026909981924334548811915, 28472531414609983697313990252890432723106104555911554183973632250910584283, 175818374607083253076391342224410067561956336707001539232918058684479529452, 1085851998647343827289114237456211031262393568472258578772559229682635463892, 6707239731370389952144273962309811101600425335202516351763022797145256602230
Specification 1
Strategy pack name: col_placements_tracked_fusion
Tree: http://permpal.com/tree/24211/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]*F[4,x]
F[3,x] = x
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[1,x]+F[6,x,k[0]]+F[8,x,k[0]]
F[6,x,k[0]] = F[3,x]*F[7,x,k[0]]
F[7,x,k[0]] = 1/(-1+k[0])*(F[5,x,k[0]]*k[0]-F[5,x,1])
F[8,x,k[0]] = F[10,x,k[0]]*F[9,x,k[0]]
F[9,x,k[0]] = k[0]*x
F[10,x,k[0]] = F[1,x]+F[11,x,k[0]]+F[17,x,k[0]]+F[27,x,k[0]]
F[11,x,k[0]] = F[12,x,1,k[0]]
F[12,x,k[0],k[1]] = F[13,x,k[0]*k[1],k[1]]
F[13,x,k[0],k[1]] = F[14,x,k[0],k[1]]*F[3,x]
F[14,x,k[0],k[1]] = 1/(-1+k[0])*(F[15,x,k[0],k[1]]*k[0]-F[15,x,1,k[1]])
F[15,x,k[0],k[1]] = F[1,x]+F[13,x,k[0],k[1]]+F[16,x,k[1],k[0]]+F[8,x,k[0]]
F[16,x,k[0],k[1]] = F[5,x,k[1]]*F[9,x,k[0]]
F[17,x,k[0]] = F[18,x,1,k[0]]
F[18,x,k[0],k[1]] = F[19,x,k[0]*k[1],k[1]]
F[19,x,k[0],k[1]] = F[20,x,k[0],k[1]]*F[9,x,k[0]]
F[20,x,k[0],k[1]] = F[1,x]+F[21,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[27,x,k[0]]+F[33,x,k[1],k[0]]
F[21,x,k[0],k[1]] = F[22,x,k[0],k[1]]*F[3,x]
F[22,x,k[0],k[1]] = (F[23,x,k[0],1]*k[0]-F[23,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[23,x,k[0],k[1]] = F[14,x,k[0],k[0]*k[1]]
F[24,x,k[0],k[1]] = F[25,x,k[0],k[1]]*F[9,x,k[0]]
F[25,x,k[0],k[1]] = (F[26,x,k[0],1]*k[0]-F[26,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[26,x,k[0],k[1]] = F[20,x,k[0],k[0]*k[1]]
F[27,x,k[0]] = F[28,x,k[0]]*F[9,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0],1]
F[29,x,k[0],k[1]] = F[30,x,k[0],k[0]*k[1]]
F[30,x,k[0],k[1]] = F[1,x]+F[16,x,k[1],k[0]]+F[21,x,k[0],k[1]]+F[24,x,k[0],k[1]]+F[31,x,k[0],k[1]]
F[31,x,k[0],k[1]] = F[32,x,k[0],k[1]]*F[9,x,k[0]]
F[32,x,k[0],k[1]] = (F[29,x,k[0],1]*k[0]-F[29,x,k[0],k[1]/k[0]]*k[1])/(-k[1]+k[0])
F[33,x,k[0],k[1]] = F[10,x,k[1]]*F[9,x,k[0]]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right) F_{4}\! \left(x \right)
F_{3}\! \left(x \right) = x
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{6}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{3}\! \left(x \right) F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = \frac{F_{5}\! \left(x , y\right) y -F_{5}\! \left(x , 1\right)}{-1+y}
F_{8}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = y x
F_{10}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{11}\! \left(x , y\right)+F_{17}\! \left(x , y\right)+F_{27}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , 1, y\right)
F_{12}\! \left(x , y , z\right) = F_{13}\! \left(x , y z , z\right)
F_{13}\! \left(x , y , z\right) = F_{14}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{14}\! \left(x , y , z\right) = \frac{F_{15}\! \left(x , y , z\right) y -F_{15}\! \left(x , 1, z\right)}{-1+y}
F_{15}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y , z\right)+F_{16}\! \left(x , z , y\right)+F_{8}\! \left(x , y\right)
F_{16}\! \left(x , y , z\right) = F_{5}\! \left(x , z\right) F_{9}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , 1, y\right)
F_{18}\! \left(x , y , z\right) = F_{19}\! \left(x , y z , z\right)
F_{19}\! \left(x , y , z\right) = F_{20}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)
F_{20}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{21}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{27}\! \left(x , y\right)+F_{33}\! \left(x , z , y\right)
F_{21}\! \left(x , y , z\right) = F_{22}\! \left(x , y , z\right) F_{3}\! \left(x \right)
F_{22}\! \left(x , y , z\right) = \frac{F_{23}\! \left(x , y , 1\right) y -F_{23}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{23}\! \left(x , y , z\right) = F_{14}\! \left(x , y , y z \right)
F_{24}\! \left(x , y , z\right) = F_{25}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)
F_{25}\! \left(x , y , z\right) = \frac{F_{26}\! \left(x , y , 1\right) y -F_{26}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{26}\! \left(x , y , z\right) = F_{20}\! \left(x , y , y z \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right) F_{9}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y , 1\right)
F_{29}\! \left(x , y , z\right) = F_{30}\! \left(x , y , y z \right)
F_{30}\! \left(x , y , z\right) = F_{1}\! \left(x \right)+F_{16}\! \left(x , z , y\right)+F_{21}\! \left(x , y , z\right)+F_{24}\! \left(x , y , z\right)+F_{31}\! \left(x , y , z\right)
F_{31}\! \left(x , y , z\right) = F_{32}\! \left(x , y , z\right) F_{9}\! \left(x , y\right)
F_{32}\! \left(x , y , z\right) = \frac{F_{29}\! \left(x , y , 1\right) y -F_{29}\! \left(x , y , \frac{z}{y}\right) z}{-z +y}
F_{33}\! \left(x , y , z\right) = F_{10}\! \left(x , z\right) F_{9}\! \left(x , y\right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x)*F_4(x))
Eq(F_3(x), x)
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_1(x) + F_6(x, k_0) + F_8(x, k_0))
Eq(F_6(x, k_0), F_3(x)*F_7(x, k_0))
Eq(F_7(x, k_0), (k_0*F_5(x, k_0) - F_5(x, 1))/(k_0 - 1))
Eq(F_8(x, k_0), F_10(x, k_0)*F_9(x, k_0))
Eq(F_9(x, k_0), k_0*x)
Eq(F_10(x, k_0), F_1(x) + F_11(x, k_0) + F_17(x, k_0) + F_27(x, k_0))
Eq(F_11(x, k_0), F_12(x, 1, k_0))
Eq(F_12(x, k_0, k_1), F_13(x, k_0*k_1, k_1))
Eq(F_13(x, k_0, k_1), F_14(x, k_0, k_1)*F_3(x))
Eq(F_14(x, k_0, k_1), (k_0*F_15(x, k_0, k_1) - F_15(x, 1, k_1))/(k_0 - 1))
Eq(F_15(x, k_0, k_1), F_1(x) + F_13(x, k_0, k_1) + F_16(x, k_1, k_0) + F_8(x, k_0))
Eq(F_16(x, k_0, k_1), F_5(x, k_1)*F_9(x, k_0))
Eq(F_17(x, k_0), F_18(x, 1, k_0))
Eq(F_18(x, k_0, k_1), F_19(x, k_0*k_1, k_1))
Eq(F_19(x, k_0, k_1), F_20(x, k_0, k_1)*F_9(x, k_0))
Eq(F_20(x, k_0, k_1), F_1(x) + F_21(x, k_0, k_1) + F_24(x, k_0, k_1) + F_27(x, k_0) + F_33(x, k_1, k_0))
Eq(F_21(x, k_0, k_1), F_22(x, k_0, k_1)*F_3(x))
Eq(F_22(x, k_0, k_1), (-k_0*F_23(x, k_0, 1) + k_1*F_23(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_23(x, k_0, k_1), F_14(x, k_0, k_0*k_1))
Eq(F_24(x, k_0, k_1), F_25(x, k_0, k_1)*F_9(x, k_0))
Eq(F_25(x, k_0, k_1), (-k_0*F_26(x, k_0, 1) + k_1*F_26(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_26(x, k_0, k_1), F_20(x, k_0, k_0*k_1))
Eq(F_27(x, k_0), F_28(x, k_0)*F_9(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0, 1))
Eq(F_29(x, k_0, k_1), F_30(x, k_0, k_0*k_1))
Eq(F_30(x, k_0, k_1), F_1(x) + F_16(x, k_1, k_0) + F_21(x, k_0, k_1) + F_24(x, k_0, k_1) + F_31(x, k_0, k_1))
Eq(F_31(x, k_0, k_1), F_32(x, k_0, k_1)*F_9(x, k_0))
Eq(F_32(x, k_0, k_1), (-k_0*F_29(x, k_0, 1) + k_1*F_29(x, k_0, k_1/k_0))/(-k_0 + k_1))
Eq(F_33(x, k_0, k_1), F_10(x, k_1)*F_9(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "place_row": false, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "col_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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